{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:MSGA2WR7APU5HHKZZNFSPBLY3P","short_pith_number":"pith:MSGA2WR7","canonical_record":{"source":{"id":"1505.01395","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-04-27T19:56:10Z","cross_cats_sorted":["math.AC","math.CO","math.IT","math.NT"],"title_canon_sha256":"988e3d694d1728c607e9764d5ef1a038598ed1d794d7b850324480f491de5571","abstract_canon_sha256":"4f73ae8b56bbd0c8a9b66d661b39ae280a6f19741ca21383d35025124d5a24ee"},"schema_version":"1.0"},"canonical_sha256":"648c0d5a3f03e9d39d59cb4b278578dbd372409ef636f76ed09c348be5963af4","source":{"kind":"arxiv","id":"1505.01395","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.01395","created_at":"2026-05-18T02:16:49Z"},{"alias_kind":"arxiv_version","alias_value":"1505.01395v1","created_at":"2026-05-18T02:16:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.01395","created_at":"2026-05-18T02:16:49Z"},{"alias_kind":"pith_short_12","alias_value":"MSGA2WR7APU5","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"MSGA2WR7APU5HHKZ","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"MSGA2WR7","created_at":"2026-05-18T12:29:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:MSGA2WR7APU5HHKZZNFSPBLY3P","target":"record","payload":{"canonical_record":{"source":{"id":"1505.01395","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-04-27T19:56:10Z","cross_cats_sorted":["math.AC","math.CO","math.IT","math.NT"],"title_canon_sha256":"988e3d694d1728c607e9764d5ef1a038598ed1d794d7b850324480f491de5571","abstract_canon_sha256":"4f73ae8b56bbd0c8a9b66d661b39ae280a6f19741ca21383d35025124d5a24ee"},"schema_version":"1.0"},"canonical_sha256":"648c0d5a3f03e9d39d59cb4b278578dbd372409ef636f76ed09c348be5963af4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:16:49.481626Z","signature_b64":"JGNPefXfDsgnjX3LrQKUwxLzxBUq+02BJV2kxjefhFLHboUu1MC5kNfqCz8/cWUr7UF/6DTs+JzlRW+Ysw4hCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"648c0d5a3f03e9d39d59cb4b278578dbd372409ef636f76ed09c348be5963af4","last_reissued_at":"2026-05-18T02:16:49.480927Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:16:49.480927Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1505.01395","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:16:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mvWdUMIK/Y/UueYdGE4nrRZVd451V8FkKHG3w7+8UCfYEdOPOEb443B13Wlknfbh4PctBzUEVNy+VomtRk2hAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T01:14:03.960094Z"},"content_sha256":"861dcc44f0eae04f411a0d611cf304e4b24264c89af673898c7b28b8b82bde2d","schema_version":"1.0","event_id":"sha256:861dcc44f0eae04f411a0d611cf304e4b24264c89af673898c7b28b8b82bde2d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:MSGA2WR7APU5HHKZZNFSPBLY3P","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The second Feng-Rao number for codes coming from inductive semigroups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC","math.CO","math.IT","math.NT"],"primary_cat":"cs.IT","authors_text":"J. I. Farr\\'an, P. A. Garc\\'ia-S\\'anchez","submitted_at":"2015-04-27T19:56:10Z","abstract_excerpt":"The second Feng-Rao number of every inductive numerical semigroup is explicitly computed. This number determines the asymptotical behaviour of the order bound for the second Hamming weight of one-point AG codes. In particular, this result is applied for the codes defined by asymptotically good towers of function fields whose Weierstrass semigroups are inductive. In addition, some properties of inductive numerical semigroups are studied, the involved Ap\\'{e}ry sets are computed in a recursive way, and some tests to check whether a given numerical semigroups is inductive or not are provided."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.01395","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:16:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DuFYQB08gPIyMn2h/wwK/PsZf8/GJsJbfT4mCqye4qGh4sEu7myHekgMNoitK/2U6ZSw143MjTZggNlf0vU8Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T01:14:03.960786Z"},"content_sha256":"97058755bde5771f9e3fd85584027b47d306e17f9677c4198d3f1957af31df71","schema_version":"1.0","event_id":"sha256:97058755bde5771f9e3fd85584027b47d306e17f9677c4198d3f1957af31df71"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MSGA2WR7APU5HHKZZNFSPBLY3P/bundle.json","state_url":"https://pith.science/pith/MSGA2WR7APU5HHKZZNFSPBLY3P/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MSGA2WR7APU5HHKZZNFSPBLY3P/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-08T01:14:03Z","links":{"resolver":"https://pith.science/pith/MSGA2WR7APU5HHKZZNFSPBLY3P","bundle":"https://pith.science/pith/MSGA2WR7APU5HHKZZNFSPBLY3P/bundle.json","state":"https://pith.science/pith/MSGA2WR7APU5HHKZZNFSPBLY3P/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MSGA2WR7APU5HHKZZNFSPBLY3P/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:MSGA2WR7APU5HHKZZNFSPBLY3P","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"4f73ae8b56bbd0c8a9b66d661b39ae280a6f19741ca21383d35025124d5a24ee","cross_cats_sorted":["math.AC","math.CO","math.IT","math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-04-27T19:56:10Z","title_canon_sha256":"988e3d694d1728c607e9764d5ef1a038598ed1d794d7b850324480f491de5571"},"schema_version":"1.0","source":{"id":"1505.01395","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.01395","created_at":"2026-05-18T02:16:49Z"},{"alias_kind":"arxiv_version","alias_value":"1505.01395v1","created_at":"2026-05-18T02:16:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.01395","created_at":"2026-05-18T02:16:49Z"},{"alias_kind":"pith_short_12","alias_value":"MSGA2WR7APU5","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"MSGA2WR7APU5HHKZ","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"MSGA2WR7","created_at":"2026-05-18T12:29:32Z"}],"graph_snapshots":[{"event_id":"sha256:97058755bde5771f9e3fd85584027b47d306e17f9677c4198d3f1957af31df71","target":"graph","created_at":"2026-05-18T02:16:49Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"The second Feng-Rao number of every inductive numerical semigroup is explicitly computed. This number determines the asymptotical behaviour of the order bound for the second Hamming weight of one-point AG codes. In particular, this result is applied for the codes defined by asymptotically good towers of function fields whose Weierstrass semigroups are inductive. In addition, some properties of inductive numerical semigroups are studied, the involved Ap\\'{e}ry sets are computed in a recursive way, and some tests to check whether a given numerical semigroups is inductive or not are provided.","authors_text":"J. I. Farr\\'an, P. A. Garc\\'ia-S\\'anchez","cross_cats":["math.AC","math.CO","math.IT","math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-04-27T19:56:10Z","title":"The second Feng-Rao number for codes coming from inductive semigroups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.01395","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:861dcc44f0eae04f411a0d611cf304e4b24264c89af673898c7b28b8b82bde2d","target":"record","created_at":"2026-05-18T02:16:49Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"4f73ae8b56bbd0c8a9b66d661b39ae280a6f19741ca21383d35025124d5a24ee","cross_cats_sorted":["math.AC","math.CO","math.IT","math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-04-27T19:56:10Z","title_canon_sha256":"988e3d694d1728c607e9764d5ef1a038598ed1d794d7b850324480f491de5571"},"schema_version":"1.0","source":{"id":"1505.01395","kind":"arxiv","version":1}},"canonical_sha256":"648c0d5a3f03e9d39d59cb4b278578dbd372409ef636f76ed09c348be5963af4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"648c0d5a3f03e9d39d59cb4b278578dbd372409ef636f76ed09c348be5963af4","first_computed_at":"2026-05-18T02:16:49.480927Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:16:49.480927Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JGNPefXfDsgnjX3LrQKUwxLzxBUq+02BJV2kxjefhFLHboUu1MC5kNfqCz8/cWUr7UF/6DTs+JzlRW+Ysw4hCw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:16:49.481626Z","signed_message":"canonical_sha256_bytes"},"source_id":"1505.01395","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:861dcc44f0eae04f411a0d611cf304e4b24264c89af673898c7b28b8b82bde2d","sha256:97058755bde5771f9e3fd85584027b47d306e17f9677c4198d3f1957af31df71"],"state_sha256":"467605a6f40c15b49f6bbee1f3a4ffdc539af5e81a5faa860238fdfad8764a48"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Hf6bATTOuAYXE5cK2545i2C6DandJIp81X6H7L+l+S/smn+qs2IKScReZQgcnsWPAVQk0IU2uVq7ey2Opw5CBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T01:14:03.964541Z","bundle_sha256":"837f135e4295b9af4ea24f35ae4a2b8f09d03b3aa61188ab35a21e0b44dd21a3"}}